This is a phase I/II study of MLN9708 for the prophylaxis of chronic graft-versus-host-disease (GVHD) in patients undergoing allogeneic hematopoietic stem cell transplantation (HSCT).

During the phase I portion, patients undergoing both sibling and unrelated donor transplantation will be enrolled on the same arm to determine the dose-limiting toxicity (DLT) and maximum-tolerated dose (MTD).

During the phase II portion of the trial, patients will be enrolled into two separate and independent cohorts: a) Matched sibling transplants and b) Unrelated donors transplants. Both cohorts will be enrolled and analyzed separately.

• For potential candidates for this trial, the recommended acute GVHD prophylaxis is a tacrolimus, methotrexate and atorvastatin combination. However, any acute GVHD prophylaxis regimen at the discretion of treating physician (not involving in vivo or ex vivo T-cell depletion, cluster of differentiation 34 (CD34) + cell selection, or post-HCT cyclophosphamide) will be permitted.
• During the phase I portion for chronic GVHD prophylaxis, four doses of MLN9708 will be administered orally (to patients undergoing either matched sibling or unrelated donor transplantation) on days 1, 8, 15 and 22, starting on day +60 to +74 post allogeneic HCT.

If zero of three patients experienced DLT at dose level 2, then it would be considered a MTD. If two or more patients experienced a DLT, dose escalation would halt and the dose level would be expanded to six patients to determine the MTD. If the dose level below already has six patients, enrolled, then it will be considered the MTD. If two or more patients experience DLT on first dose level (i.e., dose level 1), then, patients will be enrolled on dose level -1. No intrapatient dose escalation will be permitted.

• MTD is defined at maximum dose level with fewer than two of six patients experiencing DLT.
• The phase II portion will utilize the MTD for MLN9708, determined from phase I portion of the study. In phase II, patients will be enrolled in two independent cohorts of matched sibling and matched unrelated donor transplants.
• During the phase II portion, for chronic GVHD prophylaxis, four doses of MLN9708 will be administered orally on days 1, 8, 15 and 22, starting on day +60 to +90 post allogeneic HCT.

Inclusion Criteria:

1. Patients with a history of a hematological malignancy or bone marrow failure syndrome undergoing (or status post) a peripheral blood allogeneic HCT.
2. Patients aged ≥18 are eligible.
3. All patients must have received or plan to receive an allograft from a suitable human leukocyte antigens (HLA) -matched sibling or unrelated donor according to transplant center's guidelines (for selection of appropriate donor).
4. Voluntary written consent must be given before patient registration and performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care.
5. Bilirubin ≤ 2 x the upper limit of normal (ULN). For patients with Gilbert's syndrome or suspected mild veno-occlusive disease, bilirubin ≤ 3 x ULN is permitted.
6. Creatinine clearance of ≥ 30 mL/min calculated by Cockcroft-Gault equation.
7. Karnofsky performance status > 60.
8. A negative pregnancy test will be required for all women of child bearing potential. Females of child bearing potential should agree to practice 2 effective methods of contraception, at the same time, from the time of signing the informed consent form through 90 days after the last dose of study drug and must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [eg, calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception.). Breast feeding is not permitted.
9. Male patients, even if surgically sterilized (ie, status post-vasectomy), must agree to one of the following: practice effective barrier contraception during the entire study treatment period and through 90 days after the last dose of study drug, or must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, or agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence (eg, calendar, ovulation, symptothermal, post-ovulation methods] and withdrawal are not acceptable methods of contraception.)
10. No evidence of uncontrolled bacterial, viral or fungal infections at the time of enrollment.
11. No known active hepatitis B or C virus infection, or known human immunodeficiency virus (HIV) positive.

Exclusion Criteria:

1. Patients with active ≥ grade 3 peripheral neuropathy or grade 2 with pain on clinical examination during the screening period will be excluded.
2. Patients with history of allergy and/or intolerance to MLN9708 are not eligible.
3. Known GI disease or GI procedure that could interfere with the oral absorption or tolerance of MLN9708 including difficulty swallowing is not permitted.
4. Patients receiving (or status post) a cord blood or a haplo-identical allograft will not be eligible.
5. Patients undergoing (or status post) a T-cell depleted allogeneic transplantation will not be eligible.
6. Patients receiving (or status post) conditioning regimens containing antithymocyte globulin, and/or campath, one receiving post-HCT planned cyclophosphamide will not be eligible.
7. Method of stem-cell collection from the donor will be at the discretion of the treating physician. Although it is anticipated that majority of patients will receive allograft mobilized with Granulocyte- colony stimulating factor (CSF) alone; however donors receiving allografts mobilized with experimental agents (e.g. plerixafor) will remain eligible for the study.
8. Patients experiencing disease relapse (for those in complete remission at the time of HCT) or progression (for those in partial remission, stable or refractory disease at the time of HCT) will be excluded.
9. Donor lymphocyte infusions between day zero of HCT and first dose of MLN9708 are not permitted.
10. Rituximab (or other B-cell depleting monoclonal antibodies) or bortezomib administration between day zero of HCT and before the first day of MLN9708 is not permitted.
11. Patients with steroid refractory (defined as no improvement of symptoms after 7 days of systemic corticosteroids at a dose of ≥1mg/kg/day) grade II-IV acute GVHD, that is active at the time of enrollment will be excluded.
12. Patients with grade III-IV acute GVHD (even if it is not meeting criteria for steroid refractory acute GVHD), that is active at the time of enrollment will be excluded. Patients with controlled grade I-II acute GVHD can be enrolled after discussing with study PI. Topical or systemic corticosteroids therapy, as per standard of care for such grade I-II acute GVHD patients is permitted.
13. Patients with active chronic GVHD (although unlikely before day +100) will be excluded.
14. No major surgery within 14 days before enrollment.
15. No radiotherapy within 14 days before enrollment. If the involved field is small, 7 days will be considered a sufficient interval between treatment and administration of the MLN9708.
16. No evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months. Cardiac enzyme elevations for reasons other than document myocardial infarction is not an exclusion.
17. No systemic treatment, within 14 days before the first dose of MLN9708, with strong inhibitors of CYP1A2 (fluvoxamine, enoxacin, ciprofloxacin), strong inhibitors of cytochrome P450, family 3, subfamily A (CYP3A) (clarithromycin, telithromycin, itraconazole, voriconazole, ketoconazole, nefazodone, posaconazole) or strong CYP3A inducers (rifampin, rifapentine, rifabutin, carbamazepine, phenytoin, phenobarbital), or use of Ginkgo biloba or St. John's wort.
18. No serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of treatment according to this protocol.
19. No participation in other clinical trials, including those with other investigational agents within 21days of the start of this trial and throughout the duration of this trial. However co-enrollment on trials evaluating conditioning regimens, institutional protocols evaluating atorvastatin for acute GVHD prophylaxis, and stem cell collection protocols in transplant donors will be permitted. In addition patients randomized to standard-of-care (non experimental) arms of available phase II/III trials will be eligible for this study.